Arithmetic Operations
Mental Division Strategies
These strategies allow you to divide numbers quickly and confidently in your head, without needing written methods or a calculator.
1. Use Known Multiplication Facts
Division is the inverse of multiplication. If you know 8 × 7 = 56, you immediately know 56 ÷ 8 = 7.
63 ÷ 9: recall 9 × 7 = 63 → answer: 7
2. Halving for Division by 2
84 ÷ 2: 84 is 80 + 4. 80 ÷ 2 = 40. 4 ÷ 2 = 2. Total: 42
3. Repeated Halving for Division by 4 and 8
96 ÷ 4: halve twice. 96 ÷ 2 = 48. 48 ÷ 2 = 24
120 ÷ 8: halve three times. 120 → 60 → 30 → 15
4. Factoring the Divisor
252 ÷ 12: 12 = 4 × 3. 252 ÷ 4 = 63. 63 ÷ 3 = 21
5. Left-to-Right Division
840 ÷ 7: 800 ÷ 7 ≈ 114. Actually 7 into 8 = 1 r 1. 7 into 14 = 2. 7 into 0 = 0. Answer: 120
Strategy Summary Table
| Divide by | Strategy |
|---|---|
| 2 | Halve |
| 4 | Halve twice |
| 5 | Divide by 10, then double |
| 8 | Halve three times |
| 9, 7 | Use multiplication facts |
Key Takeaways
- Times table knowledge is the most powerful mental division tool.
- Repeated halving works for any power of 2.
- Factoring the divisor breaks hard divisions into two easy ones.
Practice: Use a Mental Strategy
Strategy